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How do you use the discriminant to determine the nature of the solutions given # 9m^2 + 24m + 16 = 0#?

Answer 1

Savannah Anderson

#"roots are real and equal"#

#"For any quadratic equation "ax^2+bx+c=0" the nature of the roots depends on the discriminant "Delta=b^2-4ac#

#Delta>0 " roots are real and unequal"#

#Delta=0 " roots are real and equal"#

#Delta<0 " roots are complex"#

In this case:

#9m^2+24m+16=0#

#a=9, b=24, c=16#

#Delta=24^2-4xx9xx16#

#Delta=576-576=0#

#:. " roots are real and equal"#

this can be confirmed by factorising

#9m^2+24m+16=0=>(3m+4)^2=0#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.